The T Tauri Star RY Tauri As a Case Study of the Inner Regions of Circumstellar Dust Disks

Home , Iota Tauri, RY Tauri, T Tauri, T Tauri star, Young stellar object

A&A 478, 779–793 (2008) Astronomy DOI: 10.1051/0004-6361:20077049 & c ESO 2008 Astrophysics

The T Tauri star RY Tauri as a case study of the inner regions of circumstellar dust disks

A. A. Schegerer1,S.Wolf1, Th. Ratzka2, and Ch. Leinert1

1 Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany e-mail: [email protected] 2 Astrophysikalisches Institut Potsdam, An der Sternwarte 16, 14482 Potsdam, Germany Received 3 January 2007 / Accepted 13 November 2007

ABSTRACT

Aims. We study the inner region (∼1.0 AU up to a few 10 AUs) of the circumstellar disk around the “classical” T Tauri star RY Tau. Our aim is to find a physical description satisfying the available interferometric data, obtained with the mid-infrared interferometric instrument at the Very Large Telescope Interferometer, as well as the spectral energy distribution in the visible to millimeter wavelength range. We also compare the findings with the results of similar studies, including those of intermediate-mass Herbig Ae/Be stars. Methods. Our analysis is done within the framework of a passively heated circumstellar disk, which is optionally supplemented by the effects of accretion and an added envelope. To achieve a more consistent and realistic model, we used our continuum transfer code MC3D. In addition, we studied the shape of the 10 µm silicate emission feature in terms of the underlying dust population, both for single-dish and for interferometric measurements. Results. We show that a modestly flaring disk model with accretion can explain both the observed spectral energy distribution and the mid-infrared visibilities obtained with the mid-infrared infrared instrument. We found an interesting ambiguity: a circumstellar active disk model with an added envelope, and a lower accretion rate than in the active disk model without envelope, could represent the observations equally as well. This type of model with the envelope should be considered a viable alternative in future models of other T Tauri stars. The approach of a disk with a puffed-up inner rim wall and the influence of a stellar companion is also discussed. We also investigate the influence of various fit parameters on the outcome of the radiative transfer modeling. From the study of the silicate emission feature we see evidence for dust evolution in a T Tauri star, with a decreasing fraction of small amorphous and an increasing fraction of crystalline particles closer to the star. Key words. infrared: stars – accretion, accretion disks – astrochemistry – stars: planetary systems: protoplanetary disks – radiative transfer – instrumentation: interferometers

1. Introduction However, studies of the inner circumstellar regions (∼1AU)of objects in the closest star forming regions are only feasible by T Tauri stars are known as precursors of low-mass main se- < interferometric observations. quence stars (2–3 M). In contrast to main sequence stars, their Strong emission features in the MIR range at 10 µmand characteristic properties are strong emission line radiation (e.g., 20 µm corresponding to the Si-O stretching and bending modes Balmer α) and excessive continuum radiation observed in the of silicate grains, are assumed to result from absorption and ree- UV, infrared and the millimeter (mm) wavelength range of their mission processes in optically thin dust layers of the circum- spectral energy distribution (SED). It has been shown that the stellar disks. While silicate grains are expected to be initially spatial distribution of circumstellar dust in a disk or an enve- amorphous and small (<0.1 µm; Mathis et al. 1977, MRN there- lope that is primarily exposed to stellar radiation, is responsible after)1, the crystallization of amorphous silicates starts at tem- for the excess radiation in the infrared wavelength range (e.g., peratures of ∼1200 K (e.g., Gail 1998). Moreover, high dust Adams et al. 1987), while accretion of circumstellar material re- densities and turbulent processes in the interior of circumstel- sults in the UV excess and strong emission line radiation (see lar disks favor dust grain growth to dust pebbles (e.g., Blum Hartmann 1998, for a review). et al. 2000; Johansen et al. 2005). The shape of the emitted The extraordinary interest in the inner region of a circumstel- silicate feature allows the estimation of the predominant stage lar disk results from the assumption that the formation of planets of the dust evolution in a young stellar object (YSO). Diﬀerent is favored there (see Nagasawa et al. 2006; Wünsch et al. 2005; degrees of crystallization and grain growth have already been Klahr 2004). While mm observations probe cooler outer disk re- shown in a large sample of T Tauri stars of diﬀerent ages and gions and layers close to the midplane of circumstellar disks, stellar masses (e.g., Schegerer et al. 2006). As temperature and observations in the mid-infrared (MIR) wavelength regime are density increase in circumstellar disks with decreasing distance more sensitive to warmer (250 K < T < 1000 K; see Schegerer to the central star, crystallinity and grain size sensitively depend et al. 2006: Fig. 1) disk regions, such as the surface of the in- on the radial position of the dust in a circumstellar system (e.g., ner regions where dust is directly irradiated by the central star.

Appendix A and Fig. A1 are only available in electronic form at 1 In this paper amorphous and small, i.e., primordial and interstellar http://www.aanda.org dust grains, are called not-evolved/undeveloped.

Article published by EDP Sciences and available at http://www.aanda.org or http://dx.doi.org/10.1051/0004-6361:20077049 780 A. A. Schegerer et al.: The inner regions of circumstellar dust disks

Table 1. Observed properties of RY Tau.

Parameter Value Reference RA (J2000.0) 04 21 57.41 DEC (J2000.0) +28 26 36 1 +54 Distance 134−31pc 2 Visual extinction (2.2 ± 0.2) mag 3 Spectral type F8 III 4 Stellar mass 1.69 M 5 Stellar luminosity 12.8 L 6 −8 Accretion rate 7.8 × 10 M/yr 3 Age (6.5 ± 0.9) Myr 7 References – 1: Perryman et al. (1997); 2: Bertout et al. (1999); 3: Calvet et al. (2004); 4: Mora et al. (2001); 5: Beckwith et al. (1990); 6: Akeson et al. (2005); 7: Siess et al. (1999).

Fig. 1. The spectrally resolved, calibrated visibility data derived from ff our MIDI observations (Table 3). The error bars are the 1σ deviations Table 2. Photometric measurements of RY Tau. The data of di er- that result from the observations of different calibrators in one night. ent measurements are averaged and the standard deviation is determined. For convience, all fluxes are given in Jansky and in magnitude. Conversion factors are taken from Leinert (1997).

Beckwith et al. 1999; Weidenschilling 1997; Gail 2003: Fig. 28). Wavelength [µm] Flux [Jy] ([mag]) Reference In fact, observations with MID-infrared Interferometric instru- 0.36 (U)0.04 ± 0.01 (11.72 ± 0.16) 1 ment (MIDI) have already revealed a correlation between the ra- 0.45 (B)0.14 ± 0.01 (11.23 ± 0.08) 1 dial position and the evolutionary stage of silicate dust in circum- 0.55 (V)0.33 ± 0.01 (10.12 ± 0.04) 1 / stellar disks around Herbig Ae Be (HAeBe) stars, which are the 0.64 (RC)0.59 ± 0.03 (9.3 ± 0.05) 1 more massive counterparts of T Tauri stars (Leinert et al. 2004; 0.79 (IC)1.0 ± 0.06 (8.52 ± 0.06) 1 van Boekel et al. 2004). 1.25 (J)1.6 ± 0.8(7.64 ± 0.40) 2, 3 The density, temperature and compositional structure of cir- 1.65 (H)2.3 ± 0.9(6.48 ± 0.30) 2, 3 . . ± . . ± . cumstellar dust disks and surrounding envelopes have been the 2 20 (K)38 0 5(556 0 13) 2, 3 4.80 (M)6.6 ± 2.0(3.4 ± 0.28) 4, 5 central issue of many former studies (e.g., Chiang & Goldreich . . ± . ff 11 0(N)200 0 36 1997; D’Alessio et al. 2001). Di erent modeling approaches 25 28 ± 37 have been tried to quantitatively explain and reproduce phe- 60 18 ± 47 nomenons like excess radiation, shapes of emission lines (e.g., 100 12 ± 57,8 Muzerolle et al. 2004; Natta et al. 2000), flux variations 1300 0.23 ± 0.02 9 (e.g., Herbig et al. 2003) and intensity distributions of images (e.g., Lucas et al. 1997). However, the evolution of (inner) disk References – 1: Calvet et al. (1997); 2: Gezari-Catalog (Gezari et al. 1999); 3: 2 MASS-Catalog (Cutri et al. 2003); 4: Rydgren et al. (1976); structure and its correlation to dust evolution is still unclear (e.g., 5: Elias (1978); 6: Hanner et al. (1998); 7: Strom et al. (1989); 8: Harvey Millan-Gabet et al. 2006; Beckwith et al. 1999), and has been un- et al. (1979); 9: Mora et al. (2001). derestimated in actual modeling approaches, or mainly reserved for theoretical studies (e.g., Gail 1998). However, interferometric observations in the MIR wavelength range, which are now models of Akeson et al. (2005) where near-infared (NIR) vis- available, are sensitive to the inner disk structure where warm ibilites were modeled, and discuss discrepancies. Furthermore, dust dominates. Including their sensitivity for the silicate feature, we investigate the possibility of the existence of a stellar com- the correlation between inner disk structure and grain evolution panion and compare RY Tau with HAeBe stars. Section 8 sum- can be directly studied. marizes our results. In this paper we focus on modeling of the SED and spectrally resolved N band visibilities, which we obtained for the T Tauri 2. Previous measurements star RY Tau with MIDI. The key questions of this study are the following: Is it possible to simultaneously model the SED and N RY Tau, demonstrably observed for the first time in 1907 band visibilities of RY Tau solely by an externally, i.e., passively (Pickering 1907), is a well-known T Tauri star (Joy 1945) that heated, disk? Do different extensions of this model reproduce belongs to the Taurus-Auriga molecular cloud at a distance of the observations, simultaneously? What do we learn about the ∼140 pc. Table 1 shows the main properties of this object, which (silicate) dust composition of the disk? are obtained from previous measurements. Photometric fluxes The result of previous measurements of RY Tau are pre- are listed in Table 2. sented in Sect. 2. In Sect. 3 we outline the observations of RY Tau is a UX Ori-type star, i.e., this T Tauri object has re- RY Tau and the subsequent data reduction. We present the ra- vealed irregular photometric variability in the visible and NIR diative transfer code and the basic dust set of our modeling wavelength range. During several months in 1983/84 and in approach in Sect. 4. In the following Sect. 5 we compare the 1996/97, its visible brightness increased from ∼11th to ∼9th results of the different modeling approaches we used, i.e., the magnitude and decreased again to its initial value (Herbst & ative disk model with and without an envelope, and point to Stine 1984; Zajtseva et al. 1985; Petrov et al. 1999; Herbst & supplements. In Sect. 6 the dust composition of the upper disk Shevchenko 1999). Such a rare but strong variability is conven- layers and its dependence on the radial distance from the cen- tionally explained by variations of the obscuration of the central tral star is studied. Finally, in Sect. 7 we draw comparisons be- star caused by an inclined circumstellar disk and an envelope tween the used models, refer to previous results, including the (e.g. Eiroa et al. 2002). Smaller variations (∆V ≈ 0.1, ∆J ≈ 0.2, A. A. Schegerer et al.: The inner regions of circumstellar dust disks 781

Table 3. Summary of the MIDI observations of RY Tau and calibrators. resolved interferograms and the wavelength-dependent cor- The dates, UT, L (in m) and PA (in degrees, measured from North to related flux Fcorr(λ). East) of the sky-projected baselines are listed. The airmass AM in the iii. The spectrum Ftotal(λ) is determined by single-telescope ex- right column is given for the time of fringe tracking. The observations posures that are recorded on the same detector pixels as the with a projected baseline of 79 m and 81 m provided an almost identical fringe signal Fcorr(λ). By definition, the spectrally resolved result (see Fig. 1). visibility V(λ) is obtained as the ratio of the correlated and the total flux Date UT Object L PA AM , λ Nov. 1st, 2004 3:54–4:16 HD 25604 74 96 1 68 λ = Fcorr( ) · Nov. 1st, 2004 4:37–4:56 RY Tau 79 97 1.83 V( ) (1) Ftotal(λ) Nov. 1st, 2004 4:58–5:07 RY Tau 81 95 1.79 Nov. 1st, 2004 5:54–6:10 HD 49161 64 87 1.56 This visibility is still biased by instrumental effects. Nov. 1st, 2004 7:03–7:17 HD 31421 89 82 1.28 iv. The transfer function of the instrument is determined by the observation of calibrator stars before and after the ob- Nov. 4th, 2004 0:01–0:26 HD 178345 57 146 1.42 . servation of the scientific target. A known transfer function Nov. 4th, 2004 2:19–2:47 HD 188603 46 169 2 47 is required for the elimination of the instrumental and at- Nov. 4th, 2004 3:16–3:54 HD 25604 61 117 1.75 Nov. 4th, 2004 5:11–5:29 HD 20644 59 102 1.69 mospheric influences. The calibrators are selected for their Nov. 4th, 2004 7:18–7:36 HD 37160 61 107 1.21 known diameter, the absence of strong photometric variabil- Nov. 4th, 2004 7:44–8:00 RY Tau 49 92 1.95 ities and companions, and their angular distance to the sci- Nov. 4th, 2004 9:00–9:23 HD 50778 61 113 1.04 entific target. Some of the calibrators were also used for absolute flux calibration. The error of our calibrated visibility V(λ)isthe1σ deviation that is obtained by the observations ∆K ≈ 0.2) in the range of several days were also detected (Eiroa of different calibrators in one night (see Table 3). et al. 2002). By a comparison between the maximum and minimum brightness of the object the photometric measurements, Instrumental informations and observing procedures are de- listed in Table 2, and our observations with MIDI correspond to scribed by Leinert et al. (2003b,c, 2004) and Ratzka (2005). the “quiescent” state of the object, i.e., close to the photometric minimum. 3.2. Data reduction There is a wide range of values measured for the visual extinction AV of RY Tau (Kuhi 1974: 1.3mag;Cohen& The reduction procedure of MIDI data is complex and has been Kuhi 1979: (1.9±0.2) mag; Strom et al. 1989: 0.6 mag; Beckwith described in detail by Leinert et al. (2004), Ratzka (2005), and et al. 1990: 2.7 mag; Kenyon & Hartmann 1995: 1.8 mag). We Jaffe (2004). The data obtained with MIDI were reduced with the adopt a value recently derived by Calvet et al. (1997): AV = MIA software that is based on power spectrum analysis and the (2.2 ± 0.2) mag. The level of veiling in the visible range of the results were independently confirmed by using the EWS soft- spectrum is low (<0.1; Basri et al. 1991; Hartigan et al. 1995; ware. The EWS software contains a coherent integration algo- Petrov et al. 1999) but markedly higher in the infrared range rithm, which involves a kind of shift-and-add in the complex (>0.8; Folha & Emerson 1999). plane. Both reduction software packages are publicly available2. A potential duplicity/multiplicity was not found by Leinert et al. (1993) by using NIR speckle interferometry reaching a spa- 3.3. Observational results tial resolution between 0.13 and 13 but the regular variation of the photocenter, found by the astrometric measurements of The resulting wavelength dependent visibility curves for the HIPPARCOS, could be a hint for a companion with a projected three baselines are shown in Fig. 1, including 1σ error bars. minimum distance of 3.27 AU (23.6 mas) and a position angle The spectrophotometry of the silicate emission band Ftotal(λ), of 304◦ ± 34◦ (Bertout et al. 1999). obtained during the measurements, is shown in Fig. 7, and also included in the SED of RY Tau (Fig. 6). Figure 7 also shows the observed correlated fluxes Fcorr(λ), formally obtained as a 3. Interferometric observations and data reduction product of these two quantities (Eq. (1)). We refer to the near- 3.1. Observing sequence coincidence of the observations at baseline lengths of 79 m and 81 m. RY Tau was observed with MIDI/VLTI (Very Large Telescope Interferometer; Leinert et al. 2003a) in 2004, November 1st and 4th, within the scope of guaranteed time observations. The dates 4. Tools and universal times (UT) of the observations, as well as sky- 4.1. MC3D – Monte Carlo code for radiative transfer projected baseline lengths (L) and position angles (PA) of the interferometer, are listed in Table 3. An observing sequence con- In contrast to many previous investigations where the radiative sists of the following steps: transfer function has been solved (e.g., Sonnhalter et al. 1995; Chiang & Goldreich 1997; Dullemond et al. 2001), we use the i. Single-telescope imaging is used for a highly precise acqui- well-tested code MC3D, which is based on the Monte-Carlo × sition of the object within a field-of-view of 2 2 in order method (Wolf et al. 1999; Pascucci et al. 2004). Considering an to guarantee a maximum overlap of the telescope beams. axially symmetric object, we assume a two-dimensional geom- ii. After the beam combiner is introduced into the optical etry in a polar coordinate system (r, θ) with a logarithmic grid path, the characteristic interference pattern (fringe pattern) spacing in r and a uniform grid spacing in θ. Heating sources like is found around an optical path difference (OPD) of zero. A low resolution prism (λ/δλ ≈ 30), which is put in the optical 2 http://www.mpia-hd.mpg.de/MIDISOFT/ and path of the combined beams, allows us to obtain spectrally http://www.strw.leidenuniv.nl/∼ koehler/MIA+EWS-Manual/ 782 A. A. Schegerer et al.: The inner regions of circumstellar dust disks the central star, accretion effects, and heated dust grains deter- 0.005–0.01 µm and 0.025–0.25 µm, respectively. This grain size mine the temperature distribution. The flux of the central star is power law has already been used in former modeling aproaches determined by the theoretical stellar atmosphere model provided of YSOs. We use a minimum particle size of amin = 0.005 µmin by the Kurucz (1994). The product of the dust-specific absorp- all of our modeling approaches. ffi λ tion e ciency Qabs( ), the grain surface and the blackbody emis- The maximum grain size amax affects the mass absorption sion Bν(Tdust) represent the flux that a dust grain with a temper- coefficient κν(a) of dust, i.e., κν(a) increases with a for sizes ff max ature of Tdust reemits in local thermal equilibrium (Kirchho ’s up to a few mm. The mm flux depends on the disk mass Mdisk law of local thermal equilibrium). Sources like the central star and the absorption coefficient κν(a), i.e., amax, in particular, and accretion are treated as blackbody emitters. Gas molecules when assuming an optically thin disk in the mm wavelength α and atoms are not considered in our models. range. Correspondingly, the spectral index α (Fν ∝ ν )de- The radial density distribution of the disk is given by the creases with an increase of amax from an absolute value of ∼4 surface density profile (for amax < 0.1 µm) to ∼2 (only for large bodies). The correla- −p tion between the spectral index α and the maximum dust grain Σ(r) =Σ0 · r (2) size amax was formerly studied by D’Alessio et al. (2001), while with the radial coordinate r, an exponent p and a constant Wood et al. (2002) also investigated the correlation between disk −2 mass and mm flux. Σ0 = 100 g cm (Weidenschilling 1977). The vertical density distribution is calculated self-consistently assuming hydrostatic In our modeling approach, we have found that a dust distri- equilibrium, i.e., the balance of gravitational and thermal pres- bution with a maximum grain size of amax = 0.25 µmandthe sure (Schegerer et al., in prep.). above mentioned grains size power law for silicate and carbon After temperature and density distribution have been deter- generally underestimates the mm flux unless a disk mass in the mined, the SED and the projected image of the star and its cir- range of ∼1.0 M is assumed. Circumstellar disks with such high cumstellar environment, considering an inclination angle ϑ,are masses are potentially gravitationally unstable (e.g., Laughlin calculated. The resolution of the image is by a factor of ∼10 bet- & Bodenheimer 1994; Boss 2000; Lodato & Bertin 2001). ter than the resolution of the observations. For projected base- Moreover, an upper grain size of amax = 0.25 µm results in lines of 79 m and 49 m, our observations with MIDI reached a too steep mm slope, in contrast to the measured spectral in- spatial resolutions of ∼1.8 AU and ∼2.8 AU at a distance of dex α. Using the Very Large Array for their mm measurements, ∼140 pc3. Rodmann et al. (2006) found a spectral index of α = 2.55 ± 0.09 for RY Tau and derived a maximum grain size of amax = 1mm. The latter maximum grain size is used in our modeling ap- 4.2. Dust model proach. We have to mention that the spectral index α provides The infrared excess that is emitted from YSOs originates from only a lower limit for the maximum dust size as it converges for > heated dust in the circumstellar environment. Assuming com- amax 1 mm. pact, homogeneous, and spherical dust grains, their optical Although the mm wavelength range of the observed SED can properties, such as scattering and extinction cross sections, sufficiently be simulated considering grain sizes up to 1 mm and −2 are determined by Mie scattering-theory from the measured relatively low disk masses (<10 M), the spectral contribution complex refractive index of the specific material (Bohren & in the NIR wavelength range strongly decreases with increasing Huffman 1983). In our modeling approach, we assume a dust maximum grain size. The dust particles with amax > 1 µm can be mixture of “astronomical silicate” and graphite with the rela- less effectively heated than the smaller particles of the canonical tive abundances of 62.5% for astronomical silicate and 37.5% MRN distribution5.Thiseffect is the reason why we implement for graphite (Draine & Malhotra 1993). The dielectric function a two-layer dust model in our modeling approach. The disk in- of astronomical silicate was formerly synthesized by Draine & terior contains a maximum dust grain size of 1 mm while the Lee (1984) in order to reproduce the extinction of different sili- MRN grain size distribution with amax = 0.025 µmisusedin cate compounds in interstellar space. We consider an improved the upper disk layers where the optical depth τN in N band, mea- version of this dielectric function (Weingartner & Draine 2001)4, sured vertical to the disk midplane, falls below unity. Such a which was recently confirmed by a study of the interstellar ex- division of the disk is based on the idea of the favored settling tinction in the NIR wavelength range (Indebetouw et al. 2005). of larger dust grains. Furthermore, dust particles are assumed to 1 2 κν = κν + κν ⊥ / For graphite we adopt the 3 : 3 ratio with [ ( ) 2 ( )] 3, mainly grow in the denser regions of the disk close to the mid- where and ⊥ are the components of the graphite dielectric ten- plane (e.g., Lissauer 1993; Blum & Wurm 2000). Similar disk sor for the electric field parallel and perpendicular to the crystal- models with two or more different dust layers have already been lographic c-axis and κν is the mass absorption coefficient. The proposed by Chiang & Goldreich (1997) and used by Whitney strongly absorbing graphite grains efficiently contribute to the et al. (2003), for instance. However, it is still an open question heating of the dusty circumstellar environment. The ratio of the how strongly dust grains are mixed in the circumstellar environ- extinction efficiency factor of carbon dust to the extinction effi- ment (e.g., D’Alessio et al. 1997; Gail 1998; McCabe et al. 2003; ciency factor of silicate dust is ∼10 in the NIR wavelength range Wolf et al. 2003). (Draine &Lee 1984; Wolf & Hillenbrand 2003). In order not to determine the temperature distribution of −3.5 We consider a grain size power law n(a) ∝ a with amin each single dust component and to accelerate the radiative trans- a amax,wheren(a) is the number of dust particles with radius fer simulations, we construct an “artificial” particle with optical a. This power law was formerly found by MRN studying extinc- constants that are derived by averaging the optical properties of tion of interstellar carbon and silicate with typical sizes between carbon and astronomical silicate of different sizes in each dust layer. Such an approach was justified by Wolf (2003). 3 The spatial resolution power R of an interferometer is given by the ratio of the observing wavelength λ and the sky-projected distance between a telescope pair, i.e., the effective baseline length B: R = λ/(2B). 5 For all different dust sets we assume a constant exponent of −3.5 4 See http://www.astro.princeton.edu/∼draine for the grain size power law n(a). A. A. Schegerer et al.: The inner regions of circumstellar dust disks 783

Table 4. Parameter set for the passive disk model, the active model (Sect. 5.1) and the active model with an envelope (Sect. 5.3). Results correspond to Fig. 6.

Parameter Passive disk Active disk Active disk + envelope model model model Stellar mass M 1.69 M 1.69 M 1.69 M Stellar temperature T 5560 K 5560 K 5560 K Stellar luminosity L 10.0 L 10.0 L 10.0 L −2 −3 −3 Disk mass Mdisk 1 × 10 M 4 × 10 M 4 × 10 M Outer disk radius Rout 270 AU 270 AU 270 AU Inner disk radius Rin 0.3AU 0.3AU 0.3AU Exponent p (see Eq. (2)) 1.31.31.4 Inclination ϑ <70◦ <70◦ <65◦ −5 c1 (see Eq. (5)) – – 5.0 × 10 c2 (see Eq. (5)) – – 1.0 −8 −1 −8 −1 Accretion rate M˙ –9.1 × 10 M yr 2.5 × 10 M yr Boundary temperature Tbnd – 8000 K 8000 K Truncation radius Rbnd –5R 5 R

5. Models of the density structure Königl (1991) showed that the truncation radius is not an independent quantity, but depends on stellar radius, mass, accretion In the following subsections we will present our approaches to rate and magnetic field strength. However, as we do not know model the SED and the MIR visibilities that we obtained with the exact magnetic field strength of RY Tau, we fix the boundary MIDI. An active disk model is our favorite approach. Such a temperature and truncation radius to 8000 K and 5 R, respec- model was also used to reproduce SED and K Band visibili- tively. Both values were already used for the same object by the ties of RY Tau obtained with the Palomar Testbed Interferometer study of Akeson et al. (2005) and were justified by the assumed (Akeson et al. 2005). Additionally, an active disk model with an large magnetic field of RY Tau in the range of a few kilo-Gauss. envelope and potential supplements are discussed. One of the The best fit parameters for this model are given in Table 4 main issues of this study is to clarify if the models we use can be and the model is compared to the observations in Fig. 6. The distinguished. accretion luminosity is 1.2 L. This model suffers from the fol- The existence of a passively-heated circumstellar disk in our lowing deficiency: the far-infrared (FIR) wavelength range in analysis is beyond all questions. The paradigm that the forma- the SED is slightly overestimated. A potential improvement of tion of a disk is one of the evolutionary stages of circumstel- this active disk model could be a “truncated outer disk”, for- lar stuctures has been finally confirmed by the images of many ff merly suggested by Lucas & Roche (1997) and recently used by YSOs in di erent wavelength ranges (e.g., Padgett et al. 1999; Preibisch et al. (2006). For this, the primary density distribution Mannings & Sargent 1997, 2000). The T Tauri star RY Tau is a of the disk is truncated at an outer radius RTD by multiplying the Class II object (Kenyon & Hartmann 1995) where a surrounding surface density Σ(r) (Eq. (2)) with a Fermi-type function. With a disk has already formed. Therefore, a passively heated disk is a constant C > 0 basic ingredient and will be retained in our different modeling TD Σ approaches. Σ = (r) · 6 TD(r) r (3) The disk model is characterized by the disk mass Mdisk ,the 1 + exp(CTD − CTD) RTD inner Rin and outer disk radius Rout, the inclination angle ϑ,and an exponent p, which represents the radial dependence of the This decreases the extended IR emission while the inner disk surface density Σ (see Eq. (2)). The inner radius Rin is given structure is modified much less than the outer disk regions. It in advance, but can also be considered as a starting value that could have its physical origin in a stellar companion which trun- is iterated until the temperature at the inner radius falls below cates the outer disk region. In fact, Bertout et al. (1999) pointed the the sublimation temperature of 1600 K (Duschl et al. 1996). to a potential binarity of the system. Our study has shown that Properties of the central star, like the stellar temperature T, stel- only a truncation radius of the order of 10 AU could effectively lar luminosity L and stellar mass M, are additional model pa- decrease the computed SED (Preibisch et al. 2006). However, rameters but these quantities are well constrained by previous this truncation radius is still too large to correspond to the find- studies (see Table 1). ings of Bertout et al. (1999). Moreover, such a truncation radius is so small that the MIR visibilities increase. Another possibility to decrease the extended IR emission is dust settling that re- 5.1. Active disk sults in a flattening of the flared disk as suggested by Miyake & Our active disk model is a passively heated (dust) disk where ac- Nakagawa (1995) and Dullemond & Dominik (2006). As outer cretion effects are added. The existing MC3D radiative transfer disk regions are less heated, a less effective flared disk would code therefore has to be extended. The implemented accretion also decrease the visibility. effects are briefly described in Appendix A. Studying SED and visibility, the inclination ϑ and the posi- Apart from the parameters of the disk and the star, our ac- tion angle PA of the object cannot be clearly derived. Two visibility points are not sufficient to derive these values. With respect cretion model requires three additional model parameters: ac- < ◦ cretion rate M˙ , boundary temperature Tbnd of the accreting re- to the SED only an upper limit of 65 can be determined. This gions on the surface of the star, and a magnetic truncation radius corresponds to the angle of the line of sight where the optical τ Rbnd. Defining the inner radius of the gaseous disk inside Rin, depth V in the model exceeds unity. The outer disk radius Rout = 270 AU of this model 6 We assume a gas-to-dust mass ratio of 100:1. is larger than the results from previous measurements. 784 A. A. Schegerer et al.: The inner regions of circumstellar dust disks

5.2. Inner rim wall In addition to an accretion model that is described in Sect. 5.1, Natta et al. (2001) suggested that a puffed-up wall at the inner disk rim could also produce an increased NIR excess. Dust at the inner edge of the disk is strongly heated by direct stellar irradiation. Based on the idea of hydrostatical equilibrium this heating of the inner disk edge is assumed to cause an expansion of the dust layers perpendicular to the midplane of the disk. Dullemond et al. (2001) established an analytical model of the puffed-up, inner rim wall as a supplement to the Chiang-Goldreich model (Chiang & Goldreich 1997) and defined the “inner rim scaleheight” Hrim as follows:

Hrim = χrimhin, (4) ∆ /∆ µ Fig. 2. Radial flux distribution I r for a wavelength of 8 m (solid), where χ is a dimensionless factor, larger than unity. The quan- 10 µm (dotted), 12 µm (dashed curve) and 2.4 µm (dashed-dotted rim π 2 tity hin represents the scale-height of the inner disk without curve). The mean flux I, emitted at a radius r, is multiplied with 4 r 7 and normalized by the maximum of the radial flux distribution I at a extra vertical expansion . Simulations of young stellar objects wavelength of λ = 8 µm. (YSOs) where the inner rim wall has been successfully applied, have been published by Dominik et al. (2003), Pontoppidan et al. (2005), and Eisner et al. (2005a), for instance. The repro- duction of interferometric observations in the NIR regime as- Andrews & Williams (2006) derived an outer disk radius of suming simple, analytical ring models (Millan-Gabet et al. 2001) 150 AU with the Submillimeter Array (SMA), while Rodmann has also been used as a further confirmation of the inner rim wall ff et al. (2006) found an outer disk radius of only (90±15) AU with (Natta et al. 2001). Furthermore, a pu ed-up inner rim, shadows 7-mm continuum observations at the Very Large Array (VLA). adjacent areas of the disk from direct stellar radiation (“self- ff Figure 2 shows at which stellar distances the MIR flux arises in shadowed disk”). This e ect is used to explain the spectral shape our model. This radial flux distribution confirms that it has its of the FIR excess from YSOs and to explain the classification of origin in the inner disk regions (<10 AU), mainly, that can only Group I and Group II sources (Meeus et al. 2001; Dullemond & be observed with interferometric methods. But it also shows that Dominik 2004a). Arising from a flared disk a Group I source has MIDI is not sensitive to outer disk regions (>40 AU), including a flat SED over the entire infrared wavelength range. The SED of the outer disk radius. A modeling of mm maps of this object al- a Group II source, however, strongly declines towards the FIR. lows to determine the outer disk radius but this is out of the scope Such a decline was explained by a self-shadowed disk. ff of this paper. Additionally, it should be underlined that the dis- The pu ed-up inner rim wall is still a controversial topic tribution of the NIR flux from the disk culminates at ∼1AUfor (e.g., Millan-Gabet et al. 2006). In particular, it was shown ff this model. that a pu ed-up inner rim wall does not generally emit enough −3 radiation to cause the observed NIR excess in contrast to an The disk mass of this model Mdisk = 4 × 10 M is by a factor of 3 smaller than the value that was found by Akeson envelope similar to the one that we implement in Sect. 5.3 et al. (2005). In this context we have to underline that the disk (Vinkovic´ et al. 2006). Another open issue is the static stability mass strongly depends on the dust set that is used in the model of the proposed sharp, inner rim wall (Dullemond et al. 2001). (see Sect. 4.2). The Fig. 3, left, shows the SED for our active Considering the sublimation temperature of the used dust = . µ species, Isella & Natta (2005) revised the previous inner rim disk model but with the MRN dust set (amax 0 25 m), only. ff All other model parameters are adapted. In this figure it can be model by a more rounded-o inner rim. Monnier et al. (2006) seen that the resulting flux in the mm wavelength range strongly observed RY Tau in the NIR wavelength range using the Infrared declines for a = 0.25 µm. Optical Telescope Array (IOTA) where a spatial resolution of max >1 AU has been reached, comparable to our MIDI observations. Finally, we attempted to reproduce SED and N band visibil- In fact, their modeling results were incompatible with the mod- ities with a passive disk model, solely, instead of implementing ff els possessing vertical inner walls. accretion e ects, additionally. Such passive disk models for dif- In our model the vertical density distribution is calculated ferent parameter sets were calculated but without reproducing assuming hydrostatic equilibrium. Therefore, the potential for- the SED and MIR visibilities, sufficiently. Each modeled SED ff ff mation of a pu ed-up inner wall is included in a natural way. of these simulations su ers from similar deficiencies (see upper However, it requires special computational care. In order to de- panel in Fig. 6): in contrast to the photometric measurements the ff ff λ ≈ µ µ tect the e ect of the pu ed-up inner rim wall the size of grid predicted NIR flux between 3 mand8 m is generally cells in the inner region of the disk model should be small underestimated. Moreover, the model is too strongly spatially enough. A too coarsely meshed grid results in too low, aver- resolved (visibilities which are too low) in comparison with the aged cell temperatures and in the absence of a potential puffed- measured visibilities. up inner rim wall. We use a polar coordinate system (r, θ)in This lack of NIR radiation in “naked” passive disk models our two-dimensional model with uniform steps in θ (∆θ = 1◦) was reported by Hartmann et al. in 1993. Obviously, accretion and a logarithmic scale for r (most inner step ∆r ≈ 0.01 AU). can generate the missing NIR excess in a region which cannot Therefore, the inner grid cells have an approximate size of resolved by the interferometer. In the following subsections we present two further modifications (the puffed-up inner rim wall, 7 The scale-height is defined as the vertical distance from the mid- an envelope) which have been considered to reproduce distinct plane where the density has decreased by a factor e ≈ 2.718 (Euler’s NIR excess. constant). A. A. Schegerer et al.: The inner regions of circumstellar dust disks 785

Fig. 3. Left: deficiency of the active disk model at long wavelength if only dust with standard size MRN distribution is assumed (amax = 0.25 µm; compare middle panel in Fig. 6). Observations are represented by crosses with error bars (s. Table 2). The predicted slope into the mm range is too steep. The dashed line shows the unreddened stellar flux. Right: the same as the left figure but an maximum dust grain radius of amax = 0.25 µmis assumed.

it is shown that the inner rim of our model emits only a smaller fraction of the NIR radiation. Our simulations are based on a Monte Carlo approach. Its drawback is the presence of statistical noise in the result which could in principle blur an effect such as the puffed-up inner rim wall. In order to quantify an upper limit of the scaleheight of a potential puffed-up inner rim, we assume that the scaleheight at the innermost 0.3–3 AU can be described by a quadratic polynomial (h ∝ r2). This polynomial is then fitted to the scaleheight. The corresponding standard deviation σSD between the quadratic function and the scaleheight represents the maximum height of a potential puffed-up inner rim. We get < σSD 0.002 AU which is much smaller than the value derived by Dullemond et al. (2001). The strength of the inner rim wall is still an open issue. It depends strongly on dust properties, radial disk structure and stellar Fig. 4. Scaleheight versus disk radius of our disk model from Sect. 5.1. properties that are used in the models. Future, highly spatially We do not see a puffed-up inner rim in the sense of a local maximum resolved observations in the NIR wavelength regime, that are of the scaleheight at the inner rim and a following local minimum at sensitive to the hot inner edge of the disk, will us allow to decide slightly larger radii although the rim of our model catches a large frac- to what extent the effect of a puffed-up inner disk wall exists and tion of stellar radiation. which observational effects are provoked by this phenomenon.

5.3. Active disk with a dusty envelope ∼(0.01 × 0.005) AU2. According to Dullemond et al. (2001) apuffed-up scaleheight of 0.05 AU up to 0.10 AU can be ex- Many studies (e.g., Hartmann et al. 1993; Calvet et al. 1997) pected. Figure 4 shows the scale-height of our active disk model have shown that a dusty envelope around YSOs and Class-I of Sect. 5.1. sources, in particular, substantially contributes to the observed The fact that we do not see an excessively puffed-up inner NIR excess. With respect to its optical depth a dusty envelope wall in our approach does not necessarily exclude such a phe- could even dim the stellar radiation in the visible wavelength nomenon. It is possible that the T Tauri star RY Tau is still too regime. faint. In their study Dullemond & Dominik (2004a) assumed There are also several studies which justify an envelope HAeBe stars with temperatures in the range of Teff = 10 000 K structure around the star and disk of RY Tau. Vink et al. (2003) and luminosities up to several 10 solar luminosities (see also found that changes of the polarization across the Hα line of Dominik et al. 2003). The optical depth of the inner disk re- RYTauarebasedonscatteringeffects due to an extended dusty gion also affects the formation of a rim wall. If the optical depth envelope. Direct evidence for such a circumstellar halo has is small at the inner disk region, the radiation is not absorbed been provided by R and I coronagraphic, large-scale images mainly at the inner rim of the disk but on a larger scale. In this of RY Tau (Nakajima & Golimowski 1995), in particular, and context Dullemond & Dominik (2004a) showed that the verti- NIR, scattered light images around different YSOs (e.g., Padgett cal height of the inner rim wall is notably boosted for exponents et al. 1999; Allen et al. 2002), in general. Certainly, one chal- p ≈ 4 for the surface density (Eq. (2)). Finally, the properties of lenge for interferometric studies is to decide whether the ob- the dust grains that are used in the modeling approach can also served large-scale halo around RY Tau extends down to the inner affect the inner rim as Vinkovic´ et al. (2006) mentioned. In Fig. 2 disk region. 786 A. A. Schegerer et al.: The inner regions of circumstellar dust disks

In the context of axisymmetric accretion models Ulrich (1976) created an infall model of circumstellar gas and dust in an envelope structure in order to reproduce the emission-line Hα and Hβ profiles of type I/II P Cygni objects. This ansatz has been successfully used in modeling infrared images of Class-I objects (e.g., Lucas & Roche 1997; Wolf et al. 2003). In contrast to Ulrich’s approach we add a more simple spherical dust configuration to the disk model. The spherical envelope in our model is geometrically constrained by the inner (Rin) and outer (Rout) disk radius. With the density distributions of the disk ρdisk(r,θ), of the envelope ρenv(r,θ), and the the position vector r as well as the coordinates r and θ we define − |r| c2 ρenv(r, 0) = c1 · ρdisk(Rin, 0) · (5) Rin ϑ > Fig. 5. Optical depth for a inclination of in the optical wavelength where c1 1andc2 0. The constraint c1 1 guarantees a range. For smaller inclinations the optical depth is smaller than unity low optical depth of the envelope and the possibility to observe ensuring the observations of the inner regions. However, this envelope the innermost region of the disk. Disk and envelope are com- still has effects on the SED and MIR visibilities. bined by ρ = ρ ρ < ρ (r) disk(r)for env(r) disk(r) around carbon/silicate grains can also be considered (see Fig. 1 and (6) in Chiang et al. 2001).

ρ(r) = ρenv(r)forρenv(r) >ρdisk(r). First comparisons between the silicate feature measured in laboratory experiments and observationally-based silicate spec- This assumption ensures a smooth transition from disk to enve- tra of YSOs have been drawn by Jäger et al. (1994). A widely lope. In this simple envelope + active disk model we do not im- accepted analysis to determine the silicate composition of cir- plement bipolar cavities although there are hints that such cavi- cumstellar dust is a χ2-fitting method that was established by ties, which are caused by collimated outflows, i.e. jets, generally Bouwman et al. (2001). They assumed that the silicate emission exist in YSOs (Edwards et al. 1993). Actually, the number of free feature has its origin in the optically thin surface layer of the modeling parameters should be as small as possible to ensure circumstellar disk where it results from a linear combination of that we do not overdetermine our approach. Furthermore, based mass absorption coefficient (emissivity) κi of different dust com- on images of YSOs at a similar evolutionary state as RY Tau, ponents i: Eisner et al. (2005b) mentioned that cavities have effects on the ⎛ ⎞ structure of scattered light emission, which has its maximum in ⎜ n ⎟ ν = ν, ⎜ + κ ν ⎟ , the NIR wavelength range. F( ) B( T) ⎝C0 Ci i( )⎠ (7) Figure 6 and Table 4 show the result and parameter set of i=1 our best envelope + active disk models. The accretion rate of ˙ = . × −8 −1 ∼ where C0 and Ci are fitting parameters which reflect the mass the model M 2 5 10 M yr is by a factor of 4 smaller contribution of each component i. The quantity F(ν) is the spec- than the accretion rate assumed in the previous model without tral flux at frequency ν, κ (ν) represents the frequency-dependent envelope. However, both models reproduce the SED and the vis- i mass absorption coefficient for dust component i and Bν(T)is ibilities. This result shows that both accretion and an envelope, ff the Planck function corresponding to a blackbody temperature havethesamee ects on the SED and visibilities in the NIR and T. As basic dust set for their χ2-fitting routine for T Tauri ob- MIR wavelength range. Moreover, we have to mention that the jects Schegerer et al. (2006) used the following silicate species: measurements could be reproduced without considering any ac- small (0.1 µm) and large (1.5 µm) grains of amorphous olivine, cretion effects. A comparison of these results follows in Sect. 7. . and pyroxene, as well as crystalline species such as forsterite, The accretion luminosity is 0 3 L. In the visual range and for enstatite, and quartz. inclinations ϑ < 65◦ the model is optically thin as can be seen in The single-dish spectrum Fν is measured with a single tele- Fig. 5. However the envelope evokes an observational effect on scope. For each interferometric observation of RY Tau we ob- the SED and MIR-visibilities. tained a correlated spectrum (s. Eq. (1)) which reflects the flux emitted by a region which was not spatially resolved by the in- 6. Radial gradients of the dust composition terferometer. An increasing effective baseline length of the in- in circumstellar disks terferometer results in a higher resolution. It has to be pointed out, that the single-dish spectra as well as the correlated spectra As mentioned in Schegerer et al. (2006) a more advanced disk contain spectral contributions of the silicate emission from the model considers the specific dust composition of the correspond- whole disk, but the contributions from the hotter and brighter re- ing object instead of using a canonical MRN dust set with av- gions are increasing with increasing effective baseline length. In eraged optical quantities (see Sect. 4.2). In such dust models this context a homogeneous, axial-symmetric disk is assumed. the following dust components are generally taken into account: According to the method used in Schegerer et al. (2006), we carbon, which mainly contributes to the underlying continuum find a decreasing contribution of not-evolved, i.e. amorphous, as well as amorphous and crystalline silicate dust which gen- 0.1 µm − small dust grains and an increasing crystallinity with erates the silicate features at ∼10 µmand∼20 µm. Other dust increasing baseline length, i.e. decreasing distance to the cen- species such as water ice or, more precisely, water ice mantles tral T Tauri star (see Fig. 7, Table 5). For comparison we add A. A. Schegerer et al.: The inner regions of circumstellar dust disks 787

Fig. 6. Top row: models of the spectral density distribution of RY Tau for an inclination angle of ϑ = 25◦. Here, we assume a “naked”, passively heated disk model without considering accretion effects and an envelope. Real photometric data with error bars are included in both models (see −2 Table 2). The dashed line represents the intrinsic, stellar flux. The flux Fλ is given in units W m . According to the theorem of van Cittert- Zernicke the modeled visibilities in all diagrams were calculated from the corresponding model image for the wavelengths of 8.5, 9.5, 10.6, 11.5 and 12.5 µm. Triangles and squares represent the upper and lower limit of the visibilities V(λ) for different position angles but the same inclination of the model. The measured data are included with error bars. Middle row: model of the spectral density distribution of RY Tau for an inclination of 25◦ considering accretion effects in addition to a passively heated disk. Bottom row: SED that is obtained only from an active disk model considering an envelope, additionally. the single-dish, i.e. non-correlated spectrum Fν in Fig. 7. This Table 5. Results of our χ2-fit presented in Fig. 7. The used method single-dish spectrum confirms the derived tendencies. is described in Schegerer et al. (2006) in detail. The underlying continuum is estimated by a single blackbody function with the temperature Figure 8 shows the crystallinity Ccrys, which is plotted versus the spatial resolution of our MIDI observations. The crys- T. “RMC” stands for relative mass contribution, “am.–sma.” for amorphous, 0.1 µm-small, “am.–la.” for amorphous, 1.5 µm-large and “crys.” talized material is concentrated mainly in the inner parts of the for crystalline silicate dust grains. The crystalline component includes disk (point C for highest resolution), decreases strongly with small and large silicate species: forsterite, enstatite, and quartz. See text decreasing resolution (point B for the intermediate resolution) for further discussion. and converge to a lower limit for the single-dish observation (point A) which corresponds approximately to the abundance Baseline length Resolution Silicate RMC of crystalline dust in interstellar matter (Gail 2003). The rela- am.–sma. (15 ± 3)% tive mass contribution of small dust grains decreases from the 70 AU am.–la. (82 ± 3)% A single-dish outer to the inner disk regions. Considering the used spectro- (520 mas) crys. (3 ± 1)% scopic slit we assume a resolution of 0.52 for the single-dish T (450 ± 3) K am.–sma (7 ± 3)% observations. A corresponding result was previously found by . ± van Boekel et al. (2004) for several HAeBe stars indicating 2 8AU am.–la. (82 5)% B49m (21 mas) crys. (11 ± 2)% more evolved silicate dust towards inner disk regions. Our re- T (557 ± 5) K sult shows that the formation of crystalized dust grains is also am.–sma (1 ± 1)% favored in the innermost disk region of T Tauri stars. A study 1.8AU am.–la. (80± 4)% of the absolute disk position of the crystalized dust, as for any C78m (13 mas) crys. (19 ± 2)% other material, is out of the scope of this paper and should be T (722 ± 9) K presented in a future publication. Nonetheless such a forthcom- ing study is favored by the fact that the position angles of our observations with MIDI are almost identical (Table 3), i.e. Ccrys would be an essential requirement to study the degree of radial depends only on the radial coordinate r in the disk. Such a study mixing of material in circumstellar disks described by the ratio 788 A. A. Schegerer et al.: The inner regions of circumstellar dust disks

Fig. 8. RMC of crystalized (dotted line, squares) and 0, 1 µm-small, amorphous (dashed line, triangles) silicate grains plotted versus the reached spatial resolution of our observations.

outer disk regions can also crystalize dust grains. Both, a strong radial diffusion and electric discharges in outer disk regions, respectively, would imply a shallow decrease of the crystallinity with radius. Although Fig. 8 qualitatively shows that crystalized dust grains are located mainly in the inner disk region, a further study is required to determine the absolute disk position of the crystallised dust, along with more interferometric observations with different spatial resolutions. Finally, we add a few comments on the dust set used in our modeling approach. Instead of using the canonical dust set of “astronomical silicate” and carbon, we could also use the specific silicate dust composition found by the simple linear fitting routine presented above. Preibisch et al. (2006) have already used such an approach for modeling the HAeBe star HR 5999. However, this proceeding is problematic in light of following arguments:

i. The best-fit model parameters are not sensitive to very small grains (<0.1 µm). But such tiny grains are essential for generating the observed NIR emission as Weingartner & Draine (2001) pointed out. As mentioned in Sect. 4.2, a dust set where large dust particles a > 1 µm are implemented at the expense of tiny dust grains, is very ineffective in generating NIR and MIR flux. Only additional modifications of the inner disk structure can compensate this lack of emission. However, in disk systems where the NIR flux has al- Fig. 7. Single-dish (A) and correlated spectra (B)and(C)oftheTTauri ready vanished, the substition of small grains by large grains star RY Tau (black, solid lines). The correlated spectra (B)and(C)cor- could be physically justified by advanced dust coagulation responds to a baseline length of 49 m and 78 m, respectively. The sili- (Weinberger et al. 1999; Kornet et al. 2001). cate feature are modeled by a linear combination of mass absorption co- ii. The best-fit model parameters are not sensitive to carbon. efficients κi of different amorphous and crystalline silicates (grey lines). In order to exclude remnants of the data reduction we cut the wave- The emission profile of carbon is strictly monotonic in the length interval ∼9.0 µmto∼9.7 µm influenced by the telluric ozone 10 µm-wavelength range (e.g., Wolf & Hillenbrand 2003) band. Dashed lines and dot-dashed lines represent the contribution of and thus contributes to the underlying continuum, only. If 0.1 µm- and 1.5 µm-sized, amorphous grains, respectively. The dot-dot- carbon is considered in Eq. (7), too, each potential contribu- dashed curves stand for the crystalline contribution. The underlying, tion Ccarbon of carbon would not be independent of the con- solid curves represent the continuum (here: blackbody with tempera- tribution of the single blackbody function used to reproduce ture T). the underlying continuum. iii. Apart from the analysis of the contributions of each silicate component, another important result of our 10 µm-analysis of the viscous inward and diffusive outwards stream (Wehrstedt is the derived tendency of increasing crystallinity towards & Gail 2002; Bouwman et al. 2003; Gail 2004; Pavlyuchenko inner disk regions. However, this result does not enclose the & Dullemond 2007). Moreover, such a study could give a hint determination of the absolute disk position of the crystallised whether circumstellar dust grains are only crystalized by thermal dust and it would be another requirement to use the results heating in the inner disk regions or whether electric discharges in of our χ2-fitting routine in our modeling approach. A. A. Schegerer et al.: The inner regions of circumstellar dust disks 789 iv. It has not been clear, so far, if the determined contribution by Muzerolle et al. (2004). To obtain a consistency in the mea- of each dust component corresponds to its mass fraction. As surements, they introduced an artificially puffed-up inner rim in shown in Schegerer et al. (2006) the porosity of dust grains, their modeling approach, accounting for the large NIR excesses which is not considered in our χ2-fit, affects the shape of of classical T Tauri stars, but without requiring excessive accre- the silicate feature similar to the size effect. Therefore, the tion rates. Instead of implementing such a puffed-up inner rim mass contributions of large, compact dust grains could be we assumed an envelope in our active disk + envelope where overestimated while the increasing crystallinity of the dust we assumed a smaller accretion rate (factor ∼4) than in the pure in the inner regions is still a safe conclusion (Sect. 6). active disk model. NIR flux in the model with the envelope has its origin close Only further studies can clarify if and how the results of the pre- to but outwards of the sublimation point. This extra flux results sented χ2-fitting routine can be implemented in the modeling from the stellar heating of the dust in the envelope up to the approach. sublimation temperature and in an increase of the MIR visibility corresponding to the pure active model. In contrast to pure accretion, a dusty envelope dims the cen- 7. Discussion tral star and prevents the outer disk regions from being heated too strongly by direct stellar irradiation. Therefore, the MIR ree- The main aim of this paper was to model the structure of the cir- mission from these outer regions is decreased and the spatial cumstellar environment of the T Tauri star RY Tau. In this con- ff concentration of the infrared radiation in the inner regions is in- text we presented di erent modeling approaches for the circum- creased. Such an effect caused by the envelope results in an in- stellar dust distribution (passive disk; active disk; active disk crease of the MIR visibility, in particular for measurements with + envelope) and pointed to potential supplements such as the ff the smaller projected baseline of 48 m. We have to mention that pu ed-up inner rim wall or the truncated outer disk model. An comparable effects could also be achieved by the truncation of important aim of our approach was to keep the number of model the outer disk in our active disk model or by a strongly puffed-up parameters as small as possible. With respect to our modeling inner rim. results additional parameters and modifications were only im- In contrast to our finding Akeson et al. (2005) did not find plemented if significant improvements could be obtained after- any hints for an additional envelope in their modeling approach wards. In order to decrease the mm slope of the resulting SED, for RY Tau based on NIR, interferometric observations. They the disk with the MRN dust composition of astronomical silicate suggest NIR unveiled CO absorption lines which RY Tau is ex- and carbon were replaced by a two-layer dust model where the hibiting. In fact, such unveiled CO lines could be evidence of disk interior also contains evolved, i.e. larger dust grains. the absence of a substantial envelope (Najita et al. 2003; Calvet et al. 1997). However, the almost unveiled CO absorption lines 7.1. The merits of the active disk model with and without do not necessarily exclude an envelope when considering the fol- an envelope lowing argument: The results of two-dimensional collapse calculations of the Accretion or dusty envelopes produce the additional infrared flux infalling matter in an envelope (Yorke et al. 1993) suggests a from λ ≈ 2 µmuptoλ ≈ 8 µm of the SED that is missed in the more plane-parallel than spherical envelope geometry. In this model of a “naked”, passively heated disk. model, the envelope has already collapsed at the inner disk The extra infrared radiation from the active disk model is edge. With MIDI we resolved inner disk regions with a dis- generated in the innermost disk region inwards the point of dust tance of several AU from the star (see Fig. 2) where remnants sublimation (Appendix A). The radiation which is caused by of the envelope could still exist. However, at these distances accretion additionally heats the innermost disk regions close the gas in the potential envelope is already too cold to pro- to the inner disk radius. In comparison to a “naked”, pas- vide a substantial veiling of CO lines. We point to a study of sively heated disk, the implementation of accretion effects in the Bastien & Landstreet (1979) where it was suggested that most model results in a higher spatial concentration of infrared flux of the polarization found towards RY Tau arises from a circum- in the inner region that is not spatially resolved by our MIDI stellar (dusty) envelope which actually lies outside of the high- measurement. The computed MIR visibility increases, there- temperature, gas-emitting region. Therefore, a geometry where fore (compare middle and lower panel in Fig. 6). The accretion the envelope has already disappeared at the inner edge but not rate of the model presented here (active disk without envelope), at adjacent regions could explain why the observed NIR CO ab- −8 −1 9.1 × 10 M yr , is smaller than the value found by Akeson sorption lines are unveiled and why Akeson et al. (2005) failed −7 −1 et al. (2005; 2.5 × 10 M yr ) in their model study but corre- to model photometric and NIR visibility data considering an ad- −8 −1 sponds to that of Calvet et al. (2004; 6.4 − 9.1 × 10 M yr ). ditional envelope to their pure active disk model. In fact, with The latter result is based on a multi-wavelength study in the respect to Fig. 2 the NIR emission mainly originates close to the optical-UV range considering different emission-line profiles. sublimation point. −7 −1 An accretion rate of 2.5 × 10 M yr decreases the visibilities Another potential origin of such an (not necessarily spheri- in the MIR range because of a stronger irradiation of outer disk cal) envelope could be magnetically driven disk winds contain- regions. Based on a flux ratio measurement between the contin- ing gas and, additionally, small quantities of small dust parti- uum excess and the intrinsic photospheric flux at a wavelength cles: material at the disk surface could even follow magnetical of 5700 Å, Hartigan et al. (1995) found a much lower accretion field lines for radii r which are much larger than the magneti- −8 −1 rate of M˙ ≈ 2.5 × 10 M yr in RY Tau. Vink et al. (2003) cal truncation radius r Rbnd (Appendix A) and larger than the −8 −1 determined an accretion rate of M˙ ≈ 7.5 × 10 M yr .The inner radius r > Rin (Blandford & Payne 1982). Former studies derived accretion rate from the model of Akeson et al. (2005) is assumed a correlation between the disk accretion rate M˙ onto up to a factor of 10 larger than the values that were measured the star and the outflow mass-loss rate M˙ of with M˙ of/M˙ ∼ 0.1 in the UV range. Such a discrepancy between standard accretion (Richer et al. 2000). These dust particles that follow the outflow- disk models and the measurements has been already discussed ing wind from the disk form the optically thin dusty envelope 790 A. A. Schegerer et al.: The inner regions of circumstellar dust disks assumed in our modeling approach. A possible consequence of this procedure would be the (acceleration of the) formation of an inner gap in the innermost disk region as observed in older T Tauri objects such as TW Hya (Calvet et al. 2002). Finally, we note that Fendt & Camenzind (1996) have studied stationary, axisymmetric wind flows driven by a rapidly rotating magneto- sphere. They found that the (gas) particle density in the outflow decreases with r−2.3. This result is independent from the stellar parameters (private communication with Ch. Fendt). Another origin of the dust particles in the circumstellar envelope could be hard UV irradiation from the inner accretion zone or/and the star which increases the gas temperature in the upper layers of the disk up to ∼104 K allowing the hot, gaseous material to escape from the gravitationally bound system of the star. Small dust particles accompany the gas outflow. This effect, called photoevaporation, effectively starts at a critical radius rcr where the sound speed is in the range of the escape speed, i.e. a few AU in the case of RY Tau (see Dullemond et al. 2006, for a review). However, only further theoretical studies can clear- ify if the mass loss rates of dusty material in these disk outflows is high enough to cause a sufficiently strong effect visible with MIDI. For completeness we note that gas pressure dependent photophoretic forces of light can also induce the ejection of dust from the optical thin surface layers of the disk as studied by Wurm (2005) and Wurm & Krauss (2006). YSOs of Class I (Adams et al. 1987) that reveal a circumstellar envelope + disk structure typically also show signs for accretion given that accretion is stronger for younger objects (e.g., Hartmann et al. 2005). Accretion is certainly present in RY Tau, Fig. 9. Theoretical prediction for the result obtained for the observation too, according to the mentioned, numerous studies, such as the of a stellar binary sytem with MIDI. Here, we assume two point sources, analysis of the existing Brγ and Hα lines and UV excess radi- i.e. a0(B,λ) = 1 in Eq. (8). The (normalized) visibility is shown in rela- ation. However, we have also noted that the implementation of tion with the separation of both stars (solid lines: a = 4AE;dashed + sep accretion can be totally ignored in an envelope passive disk lines: asep = 10 AE) and the projected baseline length (left: B = 49 m; model to reproduce SED and MIR visibilities. Both, accretion right: B = 79 m). The brightness ratio of the components are 1:3. In and envelope, increase the NIR- and MIR-flux. Only comple- this example the baseline of the interferometer is also parallel to the mentary observations in the UV range where the accretion rate connection line of the components. can be independently measured, will provide additional con- straints to disentangle the different model approaches and allow us to consider both accretion and the envelope in one model.

7.2. A potential stellar companion? snapshots of the system in contrast to the HIPPARCOS observations repeated on long-term. A disadvantageous conﬁguration of As mentioned in Sect. 2, Bertout et al. (1999) found indi- the secondary could actually prevent detection with the interfer- rect hints for a stellar companion analysing HIPPARCOS data. ometer. With the non-dection of a clear binary signal in our MIDI Assuming the regular motion of the photocenter of RY Tau they data, we can thus neither verify, nor disprove the existence of a derived a projected minimum distance of 3.27 AU and a position ,λ = ◦ ± ◦ companion. Assuming a0(B ) 1 for two point sources, Fig. 9 angle of 304 34 for the potential secondary. The method they shows the relation between the interferometric binary signal and used is described in Wielen (1996). the projected baseline and the separation of the objects, respec- A potential detection of a companion by interferometric ob- tively. With increasing baseline length or increasing separation servations depends on the separation asep, the position angle of the frequency of the sinusoidal variation also increases. The am- the companion with respect to the position angle of the interfer- plitude of the variation decreases with the brightness ratio of the ometric baseline and the brightness ratio arat of secondary and components. primary. The visibility of a binary system can be expressed by the approximate formula: Another aspect of this discussion is the possibility that the regular motion of the photocenter observed with HIPPARCOS 2 B in the visible range is not caused by a secondary, but by a bright- 1 + a + 2arat cos(2πasep λ ) ,λ = ,λ rat · ness irregularity in the circumstellar environment, i.e. in the disk V(B ) a0(B ) (8) / 1 + arat and or envelope. In fact, considering scattered-light images of Class I objects (Padgett et al. 1999), circumstellar envelopes, The parameter a0(B,λ) represents the visibility that results from which have their brightness maximum in the NIR and adjacent the circumstellar and -binary material assumed to be equally wavelength ranges (Wolf et al. 2003), reveal such brightness distributed around the components. A positive detection could irregularities. However, it is not clear if such a brightness ir- then be recognized by sinusoidal variation of the visibility regularity in the circumstellar environment of RY Tau is strong (Ratzka 2005). Furthermore, all interferometric observations are enough to cause the observed regular motion of the photocenter. A. A. Schegerer et al.: The inner regions of circumstellar dust disks 791

7.4. Complex interplay of disk parameters The visibility, which we try to model, is a complex function of many different disk and dust parameters. In such complex disk models the effect of any modifications of geometrical disk parameters cannot always be predicted. However, the tendencies of modifications of the main model parameters are summarized in the following:

i. An increase of the stellar effective temperature T and stellar luminosity L, in particular, mainly causes an increase of the visible and infrared flux. If the flux of the unresolved star increases more strongly than the heating of the dust and the MIR flux from the resolved circumstellar surroundings, the MIR-visibility increases. The accretion luminosity affects SED and MIR visibility, correspondingly. An increase Fig. 10. Correlation between the half light radius rH at a wavelength of of the stellar mass M corresponds to an increase of the ac- 12.5 µm and the IRAS-color at λ = 12 µmandλ = 25 µm. Plotted cretion luminosity in the active disk model (Eq. (A.2)). are the corresponding values for HAeBe objects (Leinert et al. 2004) ii. The optical depth of the disk increases with the disk mass and for RY Tau. The error bars correspond to errors of the IRAS fluxes assuming a constant outer radius. Compacter disk structure and of the interferometric measurements. The value rH of RY Tau is an decreases the averaged temperature in the inner disk region upper limit, as the active disk model predicts a too small visibility in where less MIR flux is emitted. However, the MIR flux from comparison to the measurement. outer regions simultaneously increases and the MIR visibility therefore decreases. iii. A decrease of the inner disk radius R results in more NIR 7.3. Comparison with HAeBe stars in and MIR flux and slightly increases the MIR visibility. HAeBe stars were formerly classified in Group I and Group II iv. As shown in Sect. 5.1 the outer disk radius determines the sources (Meeus et al. 2001; Sect. 5.2). Recently, Leinert FIR flux in our modeling approach. The effect of an increase et al. (2004) could explain this phenomenological classifica- of the outer radius corresponds to the effect of a decrease of tion after modeling the interferometric measurements of several the disk mass. HAeBe objects obtained with MIDI. In fact, they noticed that v. Similar to the outer disk radius, the exponent p has distinct the half light radius of their disk models in the MIR wavelength effects on the radial density distribution in the disk. Surface range8 linearly correlates with the IRAS color between 12 µm density distributions Σ with larger gradients p result in an and 25 µm, i.e. −2.5log(Fν(12 µm)/Fν(25 µm)). Circumstellar increase of the density in the inner regions of the disk. The disks around Group II sources are less flared. The geometrical MIR visibility and the infrared excess from the disk in the effect results in the outer disk regions around Group II sources NIR up to the MIR wavelength range increases, simultane- being less strongly heated than the corresponding disk regions of ously. While the FIR excess can decrease strongly at values Group I sources. Therefore, the size of the half light radius and, greater than p = 2.0, smaller exponents p < 0.8 only negli- simultaneously, the MIR color is smaller for Group II sources. gibly affect the SED and MIR visibility. Because of its stellar luminosity (L = 11.5 L) and stellar The spatial information, which we got from the MIDI observa- mass (M = 1.69 M) the T Tauri star RY Tau could be considered as a transition object between T Tauri and HAeBe stars. tions, strongly reduced the number of disk models which can As the FIR-flux declines, RY Tau can be classified as a Group II reproduce the SED. Certainly, the outer disk radius and the disk source (Meeus et al. 2001). The IRAS color of RY Tau in the mass are less constrained parameters in our models. The unique- ness of our approach cannot be proven. However, in our ap- MIR wavelength range is −2.5log(Fν(12 µm)/Fν(25 µm)) = proach we consistently verified whether the modeling results can 0, 43 ± 0, 11 (IRAS Catalogs 1985). The half light radius rH, i.e. the FWHM of the intensity distribution in our best active be improved by varying the modeling parameters. The step sizes disk model is determined here by a Gaussian fit. The intensity used for a final variation of these modeling parameters are: distribution is computed for a wavelength of λ = 12.5 µmasit ∆Rout = 10 AU, ∆Rin = 0.05 AU, is not affected by the silicate emission at this wavelength. We ∆L = 0.1 L, ∆c2 = 0.5, and ∆p = 0.1. obtain FWHM = 1.75 AU. This value is an upper limit of the half light radius as the active disk model predicts a too small For the parameter c1 and Mdisk we used: visibility in comparison to the measurement, i.e. the intensity ∆c1 = 0.1c1, and ∆Mdisk = 0.5Mdisk, distribution of the model disk decreases too slowly for increasing radii in contrast to the real intensity distribution (measure- respectively. These step sizes can be considered as an error of each resulting parameter (Table 4). As mentioned above, the stel- ment). However, with respect to the study of Leinert et al. (2004, ff Fig. 5) this result actually confirms the linear correlation for- lar mass Mstar,thee ective stellar temperature T, the accretion ˙ merly found for HAeBe stars, solely. A further correspondence rate M, the boundary temperature Tbnd and radius Rbnd as well between T Tauri and HAeBe objects has been already shown in as the visual extinction AV are constant parameters considering Schegerer et al. (2006) considering correlations between stellar previous measurements. properties and the silicate composition of the circumstellar disk of T Tauri and HAeBe objects. 8. Summary

8 The half light radius encircles the disk region emitting half of the We present interferometric observations of the classical T Tauri totally released energy in the disk. star RY Tau in the 10 µm range, which show the source well 792 A. A. Schegerer et al.: The inner regions of circumstellar dust disks

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Online Material A. A. Schegerer et al.: The inner regions of circumstellar dust disks, Online Material p 2

Appendix A: The accretion model velocity (e.g., Uchida & Shibata 1984; Bertout et al. 1988). The magnetic flux density B of a T Tauri star is in the range of ∼1– Accretion models have been studied in many publications and 3 kG (e.g., Johns-Krull et al. 2003). As the boundary radius the parameters that we used for our active disk model are well- Rbnd is assumed to be smaller than the sublimation radius of known properties of such models. However, only a few authors ≈ ff dust ( Rin for RY Tau), the accreting material in this inner re- have implemented accretion e ects in radiative transfer models gion is gaseous. Close to the stellar surface the accreting, free- (e.g., Akeson et al. 2005). It is generally assumed that the pas- falling material is abruptly stopped in one or a series of shock sive heating of the disk is the dominating source of infrared and layers. In this inner accretion zone the total released energy is mm irradiation. This is certainly true for the large scales of the ζ ˙ / ζ = − / < GM M R with 1 R (2Rbnd). Therefore, adjacent lay- disk but not for its innermost region ( 2 AU; e.g., D’Alessio ers of the shock region like the stellar photosphere are heated to et al. 1998) which can be resolved with long-baseline interfer- temperatures of Tbnd = 5700 K up to 8800 K, while temperatures ometers. We briefly summarize here the parameters of the accre- of 9000 up to 20 000 K are achieved in upper shock areas (Calvet tion disk model implemented in our approach. & Gullbring 1998). Muzerolle et al. (2004) found in their studies Former accretion disk models are generally based on the that the energy contribution from the upper shock layers can be assumption of a geometrically thin, steady disk established by < −6 −1 neglected for accretion rates M˙ 10 M yr while the stellar Lynden-Bell & Pringel (1974) and Pringle (1981). In this canon- photosphere emits most of the accretion energy. Thus, the stellar ical accretion model it is assumed that viscous stresses within the photosphere is assumed to emit the intrinsic stellar flux and the disk transport angular momentum to its outer regions. As a con- accretion energy ζGM M˙ /R. sequence of this, most of the disk material moves inward onto The crux of the accretion theory is the surface coverage fac- the protostar, while some disk matter moves outward, absorbing tor f which mimics an annulus on the stellar photosphere where all the angular momentum. Assuming a geometrically thin and the additional accretion emission occurs (D’Alessio et al. 1998; steady disk the conservation of transversal and angular momen- Bertout et al. 1988; Lynden-Bell & Pringle 1974). If a blackbody tum results in the dissipation rate D per unit area and time as a emitter is assumed, one gets: function of the radial distance from the star r: 2 4 1/2 f 4πRσT = ζGM M˙ /R. (A.3) 3GM M˙ R bnd D(r) = 1 − · (A.1) 4πr3 r The Stefan-Boltzmann constant is represented by σ.Calvet& Gullbring (1998) determined f ≈ 0.1–1.0% for HAeBe stars and The quantities G, M, M˙ , r and R are in this order: gravity con- f ≈ 10% for T Tauri stars. Stronger veiling of absorption lines stant, stellar mass, accretion rate of the infalling material, radial indicates the larger coverage factors f of T Tauri stars. distance and stellar radius. The total released energy between an In the region between the sublimation and magnetic bound- inner boundary radius of the disk Rbnd and infinity is ary radius the gradually released accretion rate in our model (see ∞ Eq. (A.1)) is determined by the accretion theory of Lynden-Bell 1 GM M˙ Ldisk = D(r)2πrdr = · (A.2) & Pringles (1974). Because of the steep decrease of the dissipa- Rbnd 2 Rbnd tion rate D with increasing distance r (see Eq. (A.1)) accretion at radial distances r > R is neglected in our model. The re- Lynden-Bell & Pringle (1974) assumed that the disk extends in maining gravitational energy of the accreting material between down to the stellar radius Rbnd = R, or to the corotation radius r = R and r = R is emitted at the stellar surface assum- where the Keplerian orbital period equals the stellar rotation pe- bnd ing a blackbody emitter with the temperature T . Note that the riod. Recent observations (e.g., Muzerolle et al. 2004) confirmed bnd effects of the boundary temperatur T and the magnetic trun- a magnetically mediated accretion processes in the innermost bnd cation radius R on the SED and MIR visibilities are marginal disk. The accretion disk is truncated by the stellar magnetic field bnd (see D’Alessio et al. 1998). A sketch of our active disk model is at a radius R of several stellar radii and material is channeled bnd showninFig.A.1. along magnetic field lines onto the star with nearly free-fall A. A. Schegerer et al.: The inner regions of circumstellar dust disks, Online Material p 3

gas & disk gas & dust

disk T*+Tbnd disk outflowing outflowing wind star wind gas gas disk disk

disk Rin Rbnd upper interior disk layers

Fig. A.1. Simpliﬁed sketch of our active disk model. The boundary temperature Tbnd, the boundary radius Rbnd and the inner disk radius Rin are shown. We use a two-layer disk model (Sect. 4.2): a disk atmosphere where the optical depth τN is smaller than unity in N band and a optical thick, disk interior.